The most taught thing to say is
はじめまして。よろしくおねがいします。<formal>
Hajimemashite. Yoroshiku onegaishimasu.
Kinda like... Pleased to meet you or how do you do. The second sentence is more like.. Let's join hands.
There are, of course, other settings.
The <standard> is
はじめまして
Hajimemashite
The <casual>
よろしく or よろしくね
Yoroshiku or yoroshiku ne
This, like I said earlier is implying "let's join hands" this is used when you're going together with someone.
the
Ne is kinda like adding an "okay?" To the end of it.